Integrals which are convex functionals

Ralph Tyrrell Rockafellar

Vol. 24 (1968), No. 3, 525–539

DOI: 10.2140/pjm.1968.24.525

Abstract

This paper examines numerical functionals defined on function spaces by means of integrals having certain convexity properties. The functionals are themselves convex, so they can be analysed in the light of the theory of conjugate convex functions, which has recently undergone extensive development. The results obtained are applicable to Orlicz space theory and in the study of various extremum problems in control theory and the calculus of variations.

Mathematical Subject Classification

Primary: 46.35

Milestones

Received: 17 August 1966

Published: 1 March 1968